TESTING/LIN/zlqt02.f(3)

🎀 TESTING/LIN/zlqt02.f(3) 🎀

Library Functions Manual, but make it bestie-friendly. This is the page for TESTING/LIN/zlqt02.f, and yes, it's giving serious LAPACK test-routine energy. 💅

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✨ NAME ✨

TESTING/LIN/zlqt02.f — that's the name, no cap. 🫶

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🌸 SYNOPSIS 🌸

Functions/Subroutines

subroutine zlqt02 (m, n, k, a, af, q, l, lda, tau, work, lwork, rwork,
     result)
     ZLQT02

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📚 Function/Subroutine Documentation 📚

subroutine zlqt02 (integer m, integer n, integer k, complex*16, dimension(
     lda, * ) a, complex*16, dimension( lda, * ) af, complex*16, dimension(
     lda, * ) q, complex*16, dimension( lda, * ) l, integer lda, complex*16,
     dimension( * ) tau, complex*16, dimension( lwork ) work, integer lwork,
     double precision, dimension( * ) rwork, double precision, dimension( * )
     result)
     ZLQT02

🎯 Purpose

Okay so here's the whole vibe: ZLQT02 tests ZUNGLQ, which generates an m-by-n matrix Q with orthonormal rows that is defined as the product of k elementary reflectors. 👑

Given the LQ factorization of an m-by-n matrix A, ZLQT02 generates the orthogonal matrix Q defined by the factorization of the first k rows of A; it compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,1:n)', and checks that the rows of Q are orthonormal. That's the whole main-character job, periodt. 💖

🧮 Parameters

• M — M is INTEGER. It's the number of rows of the matrix Q to be generated. Constraint: M >= 0.
• N — N is INTEGER. It's the number of columns of the matrix Q to be generated. Constraint: N >= M >= 0.
• K — K is INTEGER. It's the number of elementary reflectors whose product defines the matrix Q. Constraint: M >= K >= 0.
• A — A is COMPLEX*16 array, dimension (LDA,N). This is the m-by-n matrix A which was factorized by ZLQT01.
• AF — AF is COMPLEX*16 array, dimension (LDA,N). It holds details of the LQ factorization of A, as returned by ZGELQF. See ZGELQF for further details.
• Q — Q is COMPLEX*16 array, dimension (LDA,N). That's the whole description, bestie. Short and iconic.
• L — L is COMPLEX*16 array, dimension (LDA,M). Also short and iconic.
• LDA — LDA is INTEGER. It's the leading dimension of the arrays A, AF, Q and L. Constraint: LDA >= N.
• TAU — TAU is COMPLEX*16 array, dimension (M). These are the scalar factors of the elementary reflectors corresponding to the LQ factorization in AF.
• WORK — WORK is COMPLEX*16 array, dimension (LWORK). Werk, literally.
• LWORK — LWORK is INTEGER. It's the dimension of the array WORK.
• RWORK — RWORK is DOUBLE PRECISION array, dimension (M). Yes, real ones only. 💜
• RESULT — RESULT is DOUBLE PRECISION array, dimension (2). These are the test ratios: RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS ) and RESULT(2) = norm( I - Q*Q' ) / ( N * EPS ).

👑 Author

Shoutout to the author squad:

• Univ. of Tennessee
• Univ. of California Berkeley
• Univ. of Colorado Denver
• NAG Ltd.

Definition at line 133 of file zlqt02.f.

🤖 Author

Generated automatically by Doxygen for LAPACK from the source code. The robots made this page, and honestly? They ate. 🔥

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Footer vibe check, bestie: LAPACK Version 3.12.0, page TESTING/LIN/zlqt02.f(3) — that's the sign-off, and that's the whole footer. 💖✨